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The Variational Quantum Eigensolver (VQE) algorithm, as applied to findingthe ground state of a Hamiltonian, is particularly well-suited for deploymenton noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQEalgorithm with a quantum circuit ansatz inspired by the Density MatrixRenormalization Group (DMRG) algorithm. To ameliorate the impact of realisticnoise on the performance of the method we employ zero-noise extrapolation. Wefind that, with realistic error rates, our DMRG-VQE hybrid algorithm deliversgood results for strongly correlated systems. We illustrate our approach withthe Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQEhybrid methods can locate, and faithfully represent the physics of, the groundstate of such systems. Moreover, the parameterized ansatz circuit used in thiswork is low-depth and requires a reasonably small number of parameters, so isefficient for NISQ devices.

Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries